Germanium crystallographic orientation



1953 J. 5. HANSON 2,858,730

J GERMANIUM CRYSTALLOGRAPHIC ORIENTATIQN I Filed Dec. 50, 1955 5Sheets-Sheet 1 FIG.1

/ U ms INVENTOR.

' Y JAMES s. HANSON AGENT Nov. 4, 1958 J. S. HANSON GERMANIUMCRYSTALLOGRAPHIC ORIENTATION Filed Dec. 30, 1955 3 Sheets-Sheet 2 N aw NT A NH ws ms E M A J AGENT Nov. 4,,1958 J. 5. HANSON 2,858,730

GERNANIUM CRYSTALLOGRAPHIC ORIENTATION Filed Dec. =30, i955 sSheets-Sheet s 'FIG.'4"

22 21 mvsmoa I JAMES s. HANSON AG-ENTH United States Patent Thisinvention relates to semiconductor technology and in particular to amethod of orienting a monocrystalline ingot of germanium so that it maybe cut parallel to a particular crystallographic plane.

In the art of manufacturing semiconductor devices such as diodes andtransistors, it is standard practice to form the bodies of these devicesfrom portions of a large monocrystalline semiconductor ingot. Theportions of the large ingot are cut into small wafer-shaped dice andappropriate electrodes are applied to certain surfaces of the dice. Thecrystallographic structure of the monocrystalline semiconductor materialis similar to that of the diamond and is known as a body centered cubicstructure. It has recently developed in the art that a number ofadvantages in performance of semiconductor devices can be realized ifthe dicing of the monocrystalline ingotinto wafers is performed so thata particular crystallographicplane of the body centered cubic structureis parallel to the major surfaces of the die. In the case oftransistors, semiconductor wafers cut parallel to the [111]crystallographic plane have been found togive superior performance. Toprovide such crystallographic orientation in semiconductor devices it isnecessary to very accurately establish a crystallographic orientation ofthe ingot from which the wafers are cut. are grown under agitation andbecause most seed crystals from which the ingots are grown are ofuncertain orientation accuracy, if the orientation is known at all, itis difficult to find a reference plane with respect to the ingot so thatcuts that are accurately parallel to a particular crystallographic planemay be made.

This invention is directed to a novel method of optically orienting amonocrystalline germanium ingot so that a particular crystallographicaxis of the ingot will coincide with reference surfaces of the base onwhich the-ingot will eventually be mounted. Then the ingot is so'mountedwith respect, for example, to the [111] crystallographic axis, cuts madenormal to these reference surfaces will produce germanium wafers havinga [111] crystallographic plane of the cubic structure parallel to themajor faces of the wafer, and once the orientation is established theingot may be cut parallel to any desired crystallographic plane bycutting the ingot at the proper angles with respect to the referencesurfaces.

Accordingly, a primary object of this invention is to provide an opticalmeans of orienting a monocrystalline ingot so as to establish thelocation of a particular crystallographic plane within the ingot.

Another object is to provide a means of orienting a monocrystallineingot so as to establish the location of a [111] crystallographic plane.

Another object is to provide a means of mounting the monocrystallineingot for dicing normal to a particular axis of the crystal structure.

A related object is a method of determining the error angle made by acut crystal surface with respect to a particular crystollagraphic plane.

Another related object is to provide a method of form- 2,858,730Patented Nov. 4, 1958 Other objects of the invention will be pointed outin the following description and claims and illustrated in theaccompanying drawings, which disclose, by way of example, the principleof the invention and the best mode, which has been contemplated, ofapplying that principle.

' In the drawings: I

Figure 1 is a view of an octahedron crystalline structure having two ofits [111] faces corresponding to the X2 plane.

Figure 2 shows a monocrystalline germanium ingot showing the [111] planeflats and serrations.

' Figure 3 is a view of the monocrystalline ingot mounted in anorienting fixture.

Figure 4 is a technique of orientation using a narrow beam of sunlight.

- Figure 5 is another technique of orientation showing collirnatedartificial light.

Since the germanium ingots Figure 6 is a view of the oriented crystalmounted for' cutting into wafers.

It has been discovered as a germanium crystal grows into a largemonocrystalline ingot, the ingot tends to grow in the form of anoctahedron having flat areas on its surface that are parallel to the[111] crystallographic plane.

However, due to the many disturbances that can occur at freezinginterface as the monocrystalline ingot grows the true octahedron shapeis seldom readily observed in an ingot. Thus in order to establish anaccurate reference so that an ingot may be cut parallel to a particularcrystallographic plane it is necessary in the method of this inventionto position the ingot so that its [111] axis or its [100] axis coincideswith the [111] axis or [100] axis of the octahedron. The manner in whichthis is done and the reasons for the method employed will be brought outin the following description.

Considering first the [111] axis and referring to Fig-. I ure 1, anoctahedron is shown that corresponds to the ultimate shape that isapproached by the ingot. It is to be noted that all faces of theoctahedron in this position are parallel to the [1111 faces of the cubicstructure and that two of these faces correspond to the XZ plane.

, Thus flie Y axis is normal to these two faces and has ing a body for asemiconductor device having a selected been labeled the [111] axis. Theterm [111] axis is then used to designate an axis through the octahedronthat is normal to the [111] crystallographic plane. It may now be seenthat if the ingot is so oriented that its [111] axis is normal to thecutting plane, then from the geometry shown in Figure 1, cuts made inthe germanium crystal ingot from the axis will then be parallel to" the[111] plane as represented by the [111] faces of the octahedron inFigure 1 that correspond to the XZ plane. In order to do this to a highdegree of accuracy it is necessary to establish the location of the[111] axis of the'c'ry'stalline ingot. This is done in this method byreflecting a light from three equally spaced optically reflective areaslocated on the surface of one end of the ingot.

The octahedron of Figure 1 has corners labeled A, B, C, D, E 'and F. Allsurfaces correspond to [111] crystallographic plane surfaces and theplanes represented by quadrilaterals ABDE, ACEF, and BCDF correspond towhat is known in the art as the crystallographic plane.

Referring again to Figure 1, there is a first group of three [111]-planesurfaces of the octahedron labeled ACD, ABF, and BOB-respectively, eachforming the same acute angle with respect to the [111] axis and eachintersecting this axis at the same point. This angle in practice hasbeenfound to be on the order of 19 /2 and is labeled in the figure-as alpha(or); Similarly, there is a second group of three [111]-plane surfacesofthe octahedron rotated 60 about the Y or '[111] axis from the firstgroup and labeled CDE, BEF, and ADF; each plane forming the same acuteangle with the [111] axis as the first group but at a different pointfrom the first group as shown. These angles are labeled a. Angles a anda are equal. The remaining two planes of the octahedron that areparallel to the X2 plane are ABC and DEF. By virtue of the fact that allthree planes of each of these groups intersect the [111] axis at thesame angle, a light beam from a single source will be reflected to thesame position from each of the three planes of a single group if theoctahedron is rotated about the [111] axis. Then, since the crystalingot tends to grow in an octahedron shape it is possible to establishon the surface of the ingot three properly spaced optically reflectiveareas corresponding to either of the groups of planes ACD, ABF, and BCE,or CDE, BEF, and ADF.

Referring now to Figure 2 a pictorial view is presented of a typicalgermanium ingot. This ingot has been grown by the technique known asCrystal Pulling that is standard practice in the art. However, themethod of this invention, as will be apparent from the followingdiscussion, is not limited to ingots grown by a particular method sincethe octahedron shape is a property of the crystallographic structure andnot of the method of growing. The ingot 1 of Figure 2 has a body 2 ofmonocrystalline germanium that was grown from a seed crystal 3 providedwith reference surfaces 4 and 5 which will be described in detail later.On most ingots areas termed ingot flats 6 are found. A group of flatsfound near the seed 3 end of the ingot corresponds to the first group of[111] planes ACD, ABF, and BCE of the octahedron. The flats are spacedapproximately 120 apart around the ingot. Another group of flats at theopposite end of the ingot corresponds to the second group of [111]planes CDE, BEF, and ADF. The flats on the seed 3 end of the ingot arerotated 60 around the ingot from those on the opposite end. The tendencyto form flats varies tremendously from ingot to ingot; some ingots aredecidedly triangular or square depending on the crystallographicorientation of the seed, while others are almost perfect solids ofrevolution with only microscopic traces of flats. A close inspection ofthese flats reveals that they are made up of a multitude of steps,similar to a flight of stairs with the stair treads representing fairlyflat reflecting surfaces or facets parallel to a [111] plane. Thesesteps are labeled 7 in Figure 2. From the foregoing, an ingot flat mayconsist of anywhere from one or two to several hundred facets, dependingon the many disturbances that can occur at the liquidus-solidusinterface during freezing of the ingot from the melt. Thus, it can beseen that cylindrical and octahedron shapes form the two extremes ingrown monocrystalline ingots.

On an ingot in which all of the flats 6 of a particular group arepresent the facets of these areas may serve as optically reflectiveareas as described above. In a few ingots, some or even all of theseflats 6 may be missing. In such cases it is necessary to establish byartificial means the desired three optically reflective areascorresponding to one of the groups of planes of Figure 1. Where one ortwo of the necessary three flats 6 of Figure 2 are missing, theremaining flat or flats can serve as'a guide to locate those that aremissing. The missing areas can be synthesized by abrading, lapping, orsimilar means. It has been found that crystal ingots tend to exhibitfacets on the surfaces of the above described flats 6 as indicated bythe reference numeral 7 in Figure 2 and that these facets are parallelto the [111] crystallographic plane. In general these facets are of morethan suflicient reflective quality to serve as an optically reflectivearea in the desired location. The manner of properly synthesizing spacedareas with sufficient optical reflectivity where natural flats 6 aremissing will be described in detail below. The worst case would occurwhen there were no flats 6 at allon the crystal ingot and there were nofacets of sufl'icient quality to be useable. In this case, the threeflats 6 would have to be established by abrading in connection with anetching step to be described below. Some trial and error will benecessary to locate the required three properly spaced facetscorresponding to a particular group of planes but from the knowledge oftheir general location as shown in Figure 1, namely 120 spacing rotated60 from the second group of planes, the required facets may be located.

There are a group of etching reagents known in the art that arepreferential to exposing the [111] crystallographic plane. Some of thesereagents are discussed in an article by Ray C. Ellis, Jr., Etching ofsingle crystal germanium spheres-Journal of Applied Physics, vol. 25,No. 12, December 1954, pages 1497-1499. The combination known asSuperoxol (20'parts by volume H Odistilled; 5 parts by volumeHFconcentrated; and 5 parts by volume H O 37% concentrated) is a memberof this group. It has been found that a flat abraded area of an ingotwhen etched will exhibit triangular etch pits when viewed under amicroscope if the area roughly coincides with the [111] crystallographicplane and that the etch pits will be rectangular if the area roughlycoincides with the crystallographic plane. These reagents are useful indetermining whether or not an area is a [111] plane, and in connectionwith reflected light whether an area corresponds to a member of acertain group of planes, and in improving the optical quality of anarea. Thus, each area selected or provided as one of the required groupof three areas is etched to establish that it is a [111] plane, that itis a member of the proper group of planes, and to give it satisfactoryoptical quality. The preferential etch by its nature creates etch pitsurfaces that are parallel to a [111] crystallographic plane. As may beseen from Figure 1, if the etched area is not a member of the same groupof planes, the angle of reflection of a light source will be sodifferent from the angle of reflection of the other planes in the groupthat no reflection will be observed at the place in which the reflectedlight would normally fall. The optical quality of a particular area forthe purposes of this method is indicated by the quantity of directlyreflected light from the area in relation to the quantity of randomlyreflected or diffused light from the area. Since this method relies forits accuracy on a comparison of the position of a spot of lightreflected from each of the three areas the more light that is reflectedand the more sharply defined and more concentrated the spot into whichthat light is focused, the greater will be the accuracy of the method.An area is of satisfactory optical quality for this method when thelight reflected from the area forms a spot which can be easilydistinguished from the background reflected diffused light.

The ingot having the three required optically reflecting areasestablished is now positioned in a suitable fixture so that the ingotmay be adjusted for rotation about its [111] axis. An example of such afixture is shown in Figure 3 wherein the crystal 1 has a shaft 8 affixedto one end as through the use of a sealing wax or similar cement. Theshaft 8 is supported in a cylinder 9 by two sets of three screws each,respectively sets 10 and 11.

The cylinder 9 rests in a pair of V-shaped supports 12- and 13 so thatit is free to rotate about its geometric axis. The purpose of thisfixture is to permit the [111] axis of the ingot to be shifted tocoincide with the rotational axis of the cylinder 9. This isaccomplished by adjusting the two sets of screws 10 and 11.

In order to determine when the ingot is adjusted in the fixture so thatit rotates on the [111] axis use is made of the fact that the three[111] plane surfaces of one group of faces on the octahedron of Figure 1all form the same angle or. with the [111] axis. Since the ingot tendsto grow as an octahedron and since facets of the three areas have beenestablished on the surface of the ingot corresponding to these planes,then if, when the ingot is rotated, the'light from a single source isreflected from the facets of each of these three areas to the sameposition, the ingot will be rotating about the [111] axis. Two methodsof providing this light are shown in Figures 4 and 5. In both instancesan eifort has been made to provide collimated light so as to make thereflected light spot more pronounced. In Figure 4, the sun, being atalmost infinite distance provides the parallel light beam. In Figure 5an artificial light source isrrestricted by apertures to produce theparallel beam. So long as the reflected spot is distinguishable from thebackground light the'method is operable, but for accuracy a smallintense spot reflected to a target at the longest practical distance isbest.

Referring now to Figure 4, the ingot 1 is shown mounted in the fixtureas in Figure 3. A target 14 is mounted at a suitable distance from thecrystal. Six feet has been found to be a very satisfactory distance fromtarget to ingot for crystallographic orientation within i0.5 tolrance.The crystal and its fixture are mounted in such a manner that sun lightor light from some other suitably collimated source is reflected from amirror 15 to one of the required three areas on the crystal and isfurther reflected to the target 14. The crystal is then turned byrotating the cylinder 9 through approximately 120 to bring the next flatarea into position for reflection. The position of the reflected sunlight on the target will be an indication of the amount and thedirection in which the [111] axis of the crystal must be tilted to bringit into parallel with the rotational axis of the cylinder 9. Adjustmentof the two sets of screws 10 and 11 will accomplish this movement. -Thecrystal is again rotated to the third flat area and the position of thereflected light on the target is again observed and proper adjustment ofthe crystallographic axis of .the ingot is again made. This is continueduntil a reflected light spot from each of the three flat areas passes inturn through the same point on the target as the cylinder 9 is rotated.

It has been found that the smaller the flat area, the greater thedistance from the crystal to the target, and the more parallel the lightbeam, the greater the accuracy will be.

Referring now to Figure 5, a technique is shown whereby the artificialcollimated light beam is provided. In the technique of Figure 5 a light16 is provided shining through a small aperture 17 such as a hole in, apiece of cardboard onto a mirror 18. The light is reflected from themirror 18,.through a second aperture 19, to the flat areas of the ingot1, back through the aperture 19, to an observer 20 looking through a pinhole in the silver of the mirror 18. It has been found if the light 16is located around 5 to feet from the crystal 1, although once againgreater distances provide greater accuracy, and the aperture 19 islocated approximately one foot from the crystal, results at leastcomparable to the sun light method described above will be acquired.

Having oriented the crystal so that its [111] axis is parallel to theaxis of rotation, the crystal now may be mounted in a suitable fixturefor cutting, if cutting is desired. This may be seen in Figure 6 whereinthe cylinder 9 is mounted at the intersection of two sets of parallelblocks 21 and 22, and 23 and 24. The crystal 1 is mounted as through theuse of sealing wax or a suitable cement to a supporting surface so thatsaw 25 may now cut the ingot 1 at right angles to the axis of thecylinder 9 and since the cylinder axis now coincides with V the [111]axis of the ingot, the germanium wafers so obtained will have a [111]crystallographic plane parallel to the major face of the wafer.

Wafers may also be cut parallel to other desired crystallographic planesprovided the ingot is rotationally positioned about its [111] axis withrespect to the fixture reference surfaces so that a [111] facet on theingot corresponding to a particular one of a group of planes of theoctahedron of Figure 1 makes one particular angle with this referencesurface, and that the saw cut itself shall make another particular anglewith the [111] axis of the ingot. The determination of the abovementioned angles may be readily made by one skilled in the art byapplication of the geometry of the octahedron of Figure 1 to the ingot.1

At this point it is to be noted that the saw 25 may also cut seedcrystals having suflicient reference information sites so that they maybe oriented with respect to the [111] axis through the use of thesesites. A seed crystal is shown as 3 in Figure 2 and in this case thereference sites are surfaces 4 and 5, parallel to the [111] axis and atto each other. It should be understood, however, that the seed crystalis not limited to a particular shape nor are the reference sites limitedto a particular type so long as there is sufficient geometricinformation present in the reference sites or in the combination of seedcrystal shape and reference sites so that orientation with respect tothe [111] axis can be performed.-

These properly oriented seed crystals many then be used to grow [111]oriented ingots which will not require further optical orientation. Suchingots may be mounted for wafering in a manner similar to Figure 6,except that the reference information sites of the seed are utilized toestablish the [111] axis position of the ingot. It should not be notedthat rotational positioning of the ingot about the [111] axis can becontrolled by means of seeds cut from ingots that have been rotationallyoriented in accordance with the above teaching with reference to thecutting of wafers at any desired crystallographic plane. 7

Considering next the axis, from the foregoing descriptions and theoctahedron of Figure 1 it may be seen that if at least three reflectingfacets of the four are provided on-the ingot corresponding to one groupof planes ABC, BCE, CDE, and ACD or a second group of planes ABF, BEF,DEF and ADF of the octahedron of Figure 1 then it is possible to orientthe crystal by the method of this invention along a [100] axis passingthrough points F and C of the octahedron, which axis is normal to theE100] crystallographic plane ABED. Similar orientations with other [100]axes may readily be performed by one skilled in the art by applying thegeometry of the octahedron to the ingot.

It should be noted that octahedron relationships can be further utilizedby one skilled in the art in determining error angles between cutsurfaces on ingots, Wafers, etc., and the desired crystallographic planeby means of the rotational cylinder device of Figure 3, and utilizingoptical reflections from etch pit facets in the cut surfacescorresponding to the [111] octahedron plane ABC, or DEF of Figure 1.

In summary, what has been described is a method of orienting amonocrystalline germanium ingot whereby the discoveries that the ingottends to grow as an octahedron and that optically reflective areas onthe surface of the ingot are identifiable with the certain planes of theoctahedron are utilized to permit the application of thegeometricalrelationships of the octahedron to the ingot. Theserelationships then identify the position of any crystallographic planein theingot. Cutting or other operations may then be performed on theingot wit-h reference to a particular crystallographic plane, ifdesired.

While there have been shown and described and pointed out thefundamental novel features of the invention as applied to a preferredembodiment, it will be understood that various omissions andsubstitutions and changes in the form and details of the deviceillustrated and in its operation may be made by those skilled in the artwithout departing from the spirit of the invention; For example the useof X-rays or sonic vibrations may be employed instead of the preferredembodiment of light in the identification of the planes of the ingotwith the planes of the octahedron. it is the intention therefore, to belimited only as indicated by the scope of the following claims.

What is claimed is:

1. The method of positioning a germanium monocrystalline ingot on anaxis of rotation coinciding with either a [100] or a [111]crystallographic axis of said ingot, each said [100] or said [111] axisrespectively being intersected at the same angle and at essentially thesame point by at least three planes of a group of planes of thecrystalline octahedron and said [100] or said [111] axis respectivelybeing normal to a fourth [100] or [111] crystallographic plane not amember of said group comprising in combination the steps of identifyingthe location of at least three reflecting areas on said ingot each saidarea corresponding to a different plane of said group of planes of saidoctahedron, adjustably mounting said ingot for rotation, directingenergy from a single source on said ingot in the vicinity of said areasand adjusting the axis of rotation of said ingot so that energy isreflected to the same position from each of said areas as said ingot isrotated.

2. The method of positioning a germanium monocrystalline ingot on anaxis of rotation coinciding with either a [100] or a [111]crystallographic axis of said ingot, each said [100] or said [111] axisrespectively being intersected at the same angle and at essentially thesame point by at least three planes of a group of planes of thecrystalline octahedron and said [100] or said [111] axis respectivelybeing normal to a fourth [100] or [111] crystallographic plane not amember of said group comprising in combination the steps of etching saidingot with a crystallographic plane preferential etching solution,identifying the location of at least three reflecting areas on saidingot each said area corresponding to a different plane of said group ofplanes of said octahedron, adjustably mounting said ingot for rotation,di recting energy from a single source on said ingot in the vicinity ofsaid areas and adjusting the axis of rotation of said ingot so thatenergy is reflected to the same position from each of said areas as saidingot is rotated.

3. The method of orienting a germanium monoc-rystalline ingot withrespect to the [111] axis thereof, comprising in combination the stepsof determining the location of at least three reflecting areas on thesurface of said ingot, each said area being parallel with a differentplane of a corresponding group of planes of the crystalline octahedronthat intersect at the same angle and at the same point said axis, saidaxis being normal to a fourth [111] plane not a member of said group ofplanes of the crystalline octahedron, adjustably mounting said ingot forrotation, impinging light from a single source on said ingot in thevicinity of said areas and adjusting the axis of rotation of said ingotso that said light is reflected to the same position from each of saidareas when said ingot is rotated.

4. The method of orienting a germanium monocrystalline ingot withreference to the [100] crystallographic plane comprising in combinationthe steps of determining the location of at least three reflectingsurfaces on said ingot, each of said surfaces being parallel to adifferent plane of a corresponding group of planes of the crystallineoctahedron, each plane intersecting the same [100] axis at the sameangle and at the same point; said [100] axis being normal to a fourth[100] plane of said octahedron not a member of said group, adjustablymounting said ingot for rotation; impinging light from a single sourceon said ingot in the vicinity of said reflecting surfaces; and adjustingthe axis of rotation of said ingot so' that said light falls on the sameposition when reflected from each of said three surfaces in turn as saidingot is rotated.

5. The method of orienting a germanium monoc-rystalline ingot withreference to the [111] crystallographic plane comprising in combinationthe steps of identifying at least three areas on said ingot, each ofsaid areas being approximately parallel to a different plane of acorresponding group of three planes of the crystalline octahedron, eachplane intersecting the same [111] axis at the same angle and at the samepoint; said [111] axis being normal to a fourth [111] plane of saidoctahedron not a member of said group treating each of said areas with a[111] plane preferential etching solution; adjustably mounting saidingot for rotation; impinging light from'a single source on said ingotin the vicinity of said areas; and adjusting the axis of rotation ofsaid ingot so that said light is reflected to the same position fromeach of said three areas as said ingot is rotated.

6. The method of orienting a monocrystalline germanium ingot withrespect to the crystallographic plane comprising in combination thesteps of treating flat areas on the surface of said ingot with a [100]plane preferential etching solution; selecting three of said treatedareas, each selected area being parallel to a different plane of acorresponding group of three planes of the crystalline octahedron, eachplane of said group intersecting the same [100] axis of said octahedronat the same angle and at the same point; said [100] axis being normal toa fourth [100] plane of said octahedron not a member of said group,adjustably mounting said ingot for rotation; impinging light from asingle source on said ingot in the vicinity of said areas; and adjustingthe axis of rotation of said ingot so that said light is reflected tothe same position from each of said three areas when said ingot isrotated.

7. A method of acquiring suflicient information for the geometricaldetermination of the relationship of a monocrystalline ingot ofgermanium with respect to a desired crystallographic plane comprising incombination the steps of determining the location of at least threereflecting areas on the surface of said ingot, each said area beingparallel with a different plane of a corresponding group of planes ofthe crystalline octahedron, each plane of which intersects at the sameangle and at the same points a [111] axis of said octahedron; said [111]axis being normal to a fourth [111] plane of said octahedron not amember of said group, adjustably mounting said ingot for rotation;impinging light from a single source on said ingot in the vicinity ofsaid areas; adjusting the axis of rotation of said ingot so that saidlight is reflected to the same position from each of said areas whensaid ingot is rotated; and rotationally positioning said ingot so thatone of said reflecting areas is in a known position with respect to asurface parallel to said axis.

8. A method of orienting a monocrystalline ingot of germanium withrespect to a desired crystallographic plane comprising in combinationthe steps of determining the location of at least three reflecting areason the surface of said ingot, each said area being parallel with adifferent plane of a corresponding group of planes of the crystallineoctahedron that intersect a [100] axis of said octahedron at the sameangle and at the same point; said [100] axis being normal to a fourth[100] plane of said octahedron not a member of said group, adjustablymounting said ingot for rotation; impinging light from a single sourceon said ingot in the vicinity of said areas, adjusting the axis ofrotation of said ingot so that said light is reflected to the sameposition from each of said areas when said ingot is rotated, androtating one of said areas into a particular geometric relationship withsaid axis whereupon the geometric relationships applicable to saidoctahedrons are applicable to said ingot to determine the location ofsaid desired crystallographic plane within said ingot.

ReferencesCited in the file of this patent UNITED STATES PATENTS2,423,357 Watrobski July 1, 1947

1. THE METHOD OF POSITIONING A GERMANIUM MONOCRYSTALLINE INGOT ON ANAXIS OF ROTATION COINCIDING WITH EITHER A (100) OR A (111)CRYSTALLOGRAPHIC AXIS OF SAID INGOT, EACH SAID (100) OR SAID (111) AXISRESPECTIVELY BEING INTERSECTED AT THE SAME ANGLE AND AT ESSENTIALLY THESAME POINT BY AT LEAST THREE PLANES OF A GROUP OF PLANES OF THECRYSTALLINE OCTAHEDRON AND SAID (100) OR SAID (111) AXIS RESPECTIVELYBEING NORMAL TO A FOURTH (100) OR (111) CRYSTALLOGRAPHIC PLANE NOT AMEMBER OF SAID GROUP COMPRISING IN COMBIANTION THE STEPS OF IDENTIFYING